Hi
I cant speak interms of the mathematical definition but my undestanding tells me that all signal components are delayed when passed through a device such an amplifier or a loudspeaker or as propagating though space or a medium, such as air. This delay can be different for different frequencies if the device is not LINEAR PHASE.A linear phase filter has constant group delay, all frequency components have equal delay times. That is, there is no distortion due to the time delay of frequencies relative to one another.
Thanks & Regards
Akella